Oats are probably one of the healthiest treats you can give them. I wouldn't worry about the amounts too much while you're hand taming them (unless they're going through a whole packet of Quakers oats! Which I doubt they could do even if they wanted to! lol). Things like nuts and seeds can be used every now and then in smaller amounts, but oats win with most degus.
You could try healthier things like herbs too as some degus go mad for them! You can get apple wood chew sticks of the internet and my boys like to play 'tug of war' at playtime out of the cage with these. Just remember to let them win! They'll run off with the stick and when they drop it, pick it back up and play the same game with them I've found this to be a 'healthy' way to bond with them. They might tell you off if you don't let them win the stick off you quickly though!
This is very interesting and maybe a cultural difference. Porridge oats are used here mainly to feed up ill degus as they contain quite a high amount of energy and fat. In general, they are better than other cereals but nevertheless should not be fed in higher amounts. At least this is what I learnt. You could try fresh and dried flowers, herbs (mine go crazy for basil) and fresh or dried dandelion roots.
When a human decides to adopt/buy an animal than it is a predictable time for the human.
For the animal, however, it is all it has: It is his life!